Effects of intense optical phonon pumping on the structure and electronic properties of yttrium barium copper oxide

We investigate the structural modulations induced by optical excitation of a polar phonon mode in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ using first-principles calculations based on density functional theory. We focus on the intense-excitation regime in which we expect that fourth-order phonon-phonon coupling terms dominate and model the structural modulations induced by pulses of such intensity. Our calculations of the phonon-phonon anharmonicities confirm that the cubic coupling between modes, shown in earlier work to cause a quasistatic change in the apical O-Cu distance and a buckling of the ${\mathrm{CuO}}_2$ planes, is the leading contribution at moderate pump strengths. At higher pump strengths ($\sim 10\mathrm{MV}/\mathrm{cm}$) the previously neglected quartic couplings become relevant and produce an additional shearing of the ${\mathrm{CuO}}_2$ planes. Finally, we analyze the changes in the electronic and magnetic properties associated with the induced structural changes.

Figure 1

Eigendisplacements of selected phonon modes in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$; the black arrows indicate the relative atomic displacements. (a) The pumped polar $B_{1u}$(17) phonon mode, (b) the symmetry-conserving $A_g$(14) phonon mode, and (c) the in-plane mode $B_{2g}$(2).

Figure 2

Calculated potential landscapes $V(Q_{{\mathrm{IR}}_{}},Q_{{\mathrm{G}}_{}})$ as a function of the $G$ mode amplitude for different IR mode amplitudes. (a) Cubic coupling of the polar $B_{1u}$(17) and $A_{1g}$(14) modes. Excitation of the IR mode displaces the potential minimum for the $G$ mode to a nonzero value. (b) Quartic coupling of the $B_{1u}$(17) and $B_{2g}$(2) modes. The $G$-mode potential softens for small IR amplitude and evolves into a symmetric double well with minima at nonzero $G$ mode amplitude at large IR amplitude.

Figure 3

(a) Time evolution of the $B_{1u}$(17) (blue dashed line) and $A_g$(14) (solid orange line) phonon modes after excitation of the $B_{1u}$(17) mode by a pulse $F\left(t\right)$ (pulse envelope shown by dotted green line). (b) Fourier transform of the time-dependent amplitudes from (a). The straight lines mark the eigenmode frequencies of the uncoupled $A_g$(14) and $B_{1u}$(17) modes. (c) Maximal amplitudes of the $B_{1u}$(17) and $A_g$(14) modes and average amplitude of the $A_g$(14) mode as a function of pump strength $F$ relative to the reference $F_R$. (d) Time evolution of the $B_{1u}$(17) (blue dashed line) and $A_g$(14) (solid orange line) modes after excitation with a pulse of strength $2.5F_0$. (e) Maximal and average amplitudes as a function of pulse width $\sigma$ relative to the value used in the previous calculation, ${\sigma }_0=0.18$ ps. (f) Maximal and average amplitudes as a function of pulse frequency $\omega$ relative to the resonance frequency of the $B_{1u}$(17) mode ${\omega }_0=17\mathrm{THz}$.

Figure 4

Calculated densities of states at the Fermi level $N_{E_F}$ as a function of (a) the $A_g$(14) mode amplitude and (b) the $B_{1u}$(17) mode amplitude. The dashed vertical lines indicate the values of the averaged $A_g$(14) mode amplitude [in (a)] and $B_{1u}$(17) maximum amplitude [in (b)] at our reference pump strength.

Figure 5

(a) Schematic of the two copper-oxygen planes of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ indicating the two magnetic exchanges, $J_{\mathrm{inter}}$ and $J_{\mathrm{intra}}$, that we consider in this work. Calculated magnetic exchange interaction as a function of mode amplitude for (b) $A_g$(14), (c) $B_{1u}$(17), and (d) $B_{2g}$(2) mode amplitudes. The vertical dashed lines in (b) and (c) indicate the values of average and maximum mode amplitude induced by the reference pulse for $A_g$(14) and $B_{1u}$(17), respectively. In (d) the vertical lines show the induced maximum amplitude of $B_{2g}$(2) after excitation of the system with a field pulse four times stronger than the reference pulse. Note the different $y$-axis scales.

Figure 6

(a) Time evolution of the $B_{1u}$(17) (blue dashed line) and $B_{2g}$(2) (orange line) phonon modes after excitation of the $B_{1u}$(17) mode by a pulse $F\left(t\right)$ (pulse envelope shown by the dotted green line). (b) Fourier transform of the time-dependent amplitudes in (a). The straight lines mark the mode frequencies of $B_{2g}$(2) and $B_{1u}$(17). Note that the spectra of $B_{2g}$(2) is scaled by a factor of 100. (c) Maximum amplitudes of the $B_{2g}$(2) and $B_{1u}$(17) modes after excitation with different pulse strengths $F$ given relative to the reference value $F_0=3$ MV/cm. (d) Oscillation frequencies $f$ of the $B_{2g}$(2) and $B_{1u}$(17) modes (relative to their unperturbed eigenfrequencies $f_0$) as a function of excitation pulse strength. Time evolution of the $B_{2g}$(2) mode for a range of $B_{1u}$(17) mode pulse strengths (e) below and (f) above the critical strength at which the frequency of the $B_{2g}$(2) mode becomes zero. Note that the time range is extended with respect to that shown in (a).